The \(\mathbb{A}_{q,t}\) algebra and parabolic flag Hilbert schemes

DOI10.1007/s00208-019-01898-1zbMath1441.16045arXiv1710.01407OpenAlexW2999446582WikidataQ114692899 ScholiaQ114692899MaRDI QIDQ2308331

Anton Mellit, Erik Carlsson, Eugene Gorsky

Publication date: 3 April 2020

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.01407

Mathematics Subject Classification ID

Parametrization (Chow and Hilbert schemes) (14C05) Graded rings and modules (associative rings and algebras) (16W50) Hermitian (K)-theory, relations with (K)-theory of rings (19G38) Orthogonal polynomials and functions associated with root systems (33C52) Derived categories and associative algebras (16E35) Combinatorial aspects of groups and algebras (05E16) Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) (57K18)

Related Items

Homology of torus knots, Hecke correspondences for smooth moduli spaces of sheaves, THE STABLE LIMIT DAHA AND THE DOUBLE DYCK PATH ALGEBRA, Rectangular analogues of the square paths conjecture and the univariate Delta conjecture

Cites Work

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• Refined knot invariants and Hilbert schemes
• Equivariant \(K\)-theory of Hilbert schemes via shuffle algebra
• Yangians and cohomology rings of Laumon spaces
• Quantum affine Gelfand-Tsetlin bases and quantum toroidal algebra via \(K\)-theory of affine Laumon spaces
• Parabolic bundles as orbifold bundles
• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• A combinatorial formula for the character of the diagonal coinvariants
• Parameterizing Hecke algebra modules: Bernstein-Zelevinsky multisegments, Kleshchev multipartitions, and crystal graphs.
• Affine Hecke algebras and generalized standard Young tableaux.
• A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion
• The elliptic Hall algebra and the \(K\)-theory of the Hilbert scheme of \(\mathbb{A}^{2}\)
• Toric braids and \((m,n)\)-parking functions
• Homology of torus knots
• Hecke correspondences for smooth moduli spaces of sheaves
• Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology
• A Schur-Weyl like construction of the rectangular representation for the double affine Hecke algebra
• Some new applications of the Stanley-Macdonald Pieri Rules
• Moduli of flags of sheaves and their K-theory
• A combinatorial formula for nonsymmetric Macdonald polynomials
• Equivariant K-Theory and Representations of Hecke Algebras
• Lectures on K-theoretic computations in enumerative geometry
• A proof of the shuffle conjecture